Programming with MATLAB to color latin squares

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-04-0058

Keywords:

Latin square, Transversal, Partial transversal, Chromatic number, Dihedral group

Abstract

With a Matlab programming we will find the chromatic number for all Latin squares of order smaller than 7. Previously, a manual algorithm for coloring the Latin square was provided. This algoritm determined the chromatic number of some special classes of Latin squares such as Cyclic or Dihedral, so, we tried to speed up the process of this algorithm with a programming.

Author Biographies

A. Shokri, Islamic Azad University- South Tehran Branch.

Dept. of Mathematics

M. Golriz, Islamic Azad University- South Tehran Branch.

Dept. of Mathematics.

M. Alaeiyan, Iran University of Science and Technology.

Dept. of Mathematics.

References

N. Besharati, L. Goddyn, E. S. Mahmoodian, and M. Mortezaeefar, “On the chromatic number of latin square number of latin square graphs”, Discrete mathematics, vol. 339, no. 11, pp. 2613-2619, Nov. 2016, doi: 10.1016/j.disc.2016.04.025

T. Mora, Ed., Applied algebra, algebraic algorithms and error-correcting codes. Berlin: Springer, 1989, doi: 10.1007/3-540-51083-4

M. Mortezaeefar, “Colorings of latin square graphs and block designs”, Master’s thesis, Sharif University of Technology, 2009.

K. Shokri, "On the latin square of groups and their coloring", Master’s thesis, Sharif University of Technology, 2015.

A. Shokri and M. Golriz, “A new algorithmic method to compute the chromatic number of dihedral group”, in press.

I. Wanless, “Transversals in latin squares: a survey,” in Surveys in Combinatorics 2011, R. Chapman, Ed. Cambridge: Cambridge University Press, 2011, pp. 403–437, doi: 10.1017/CBO9781139004114.010

Published

2020-07-28

How to Cite

[1]
A. Shokri, M. Golriz, and M. Alaeiyan, “Programming with MATLAB to color latin squares”, Proyecciones (Antofagasta, On line), vol. 39, no. 4, pp. 933-943, Jul. 2020.

Issue

Vol. 39 No. 4 (2020): Special Issue: Mathematical Computation in Combinatorics and Graph Theory

Section

Artículos

Copyright (c) 2020 A. Shokri, M. Golriz, M. Alaeiyan

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

  • No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.